A vector-like top partner plays a central role in many new physics models that attempt to address the hierarchy problem. The top partner is conventionally assumed to decay to a quark and a Standard Model (SM) boson. However, it is also possible that the top partner decays to a non-SM scalar and a top quark. Such an exotic decay channel can be the main decay channel of top partners, and thus provides new windows to search for top partners at the LHC. In this paper, with the classical machine learning method of boosted decision trees, we perform a model-independent study of the discovery potential of this new signature at the LHC. In order to suppress the main QCD background, we consider the subdominant but clean decay channel $a\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$. For completeness, the single production process and pair production process of top partners are taken into account. We find that, for both single and pair production, the future high-luminosity LHC can exclude a top partner mass up to the TeV scale through the channel $T\ensuremath{\rightarrow}ta$ ($a\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$), even if $\mathrm{BR}(a\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})$ is as small as $\mathcal{O}(0.1%)$. Besides, our result shows that single production can overmatch pair production at the 14 TeV LHC, provided that the top partner is heavier than 800--900 GeV.